Question

factorize: 27x³ + 125y³ . (class 9th)

Answer 1

$27x^{3} + 125y^{3}$

$= (3x)^{3} + (5y)^{3}$

/* By algebraic identity */

$\boxed{\pink{a^{3} + b^{3} = (a+b)(a^{2}-ab+b^{2}}}$

$= (3x+5y)[ (3x)^{2}- (3x)(5y) + (5x)^{2} ]$

$= (3x+5y)( 9x^{2} - 15xy + 25x^{2} )$

Therefore.,

$\red{Factors \: of \: 27x^{3} + 125y^{3}}$

$\green {= (3x+5y)( 9x^{2} - 15xy + 25x^{2} )}$

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